A single step of a supply curve, parameterised in the representation of quantities of goods. Note that the step length is relative, i.e. the width of this single step rather than the total number of units sold up to this point.

A supply "curve" is in fact a step function, with the price increasing at each step. A final price may optionally be specified, indicating that there is an unlimited quantity available at that price.

Quantities are those for the good to which this supply curve belongs, and all later goods (if any). Prices are expressed relative to the preceding good (or to "no sale", if there is no preceding good).

Make a supply curve with no quantity available at all.

Make a single-step supply curve with a fixed quantity available and no price margin over the previous good.

Make a stepped supply curve with a finite total quantity (i.e. going off vertically to infinity). Steps of width 0 will be ignored.

Make a stepped supply curve with an infinite quantity available (i.e. going off horizontally to infinity). Steps of width 0 will be ignored.

This is not fully supported and may be removed.

Make a supply curve with an optional final price, filtering out any zero-width steps.

View a supply curve as a list of indexed steps, satisfying the invariant that only the final step may have Nothing for the quantity.

Total quantity available in (the finite part of) the supply curve, i.e. the total width of the steps.

Render a supply curve as a list of (quantity, price) pairs.

Check that a supply curve is non-decreasing.

Extract the (first) reserve price from a supply curve. Returns Nothing if the supply curve has no steps.

The supply for an auction consists of:

• a set of goods (represented by the domain of the map);
• a partial order on this set (represented by listing the covers for each good, i.e. its immediate successors);
• a SupplyCurve for each good, expressing how the reserve price relative to the previous good increases as the quantity sold of this good and all larger goods increases.

The partial order must be a subset of the total order induced by the Ord instance on goods (i.e. if j1 has a cover j2 then we must have j1 < j2 == True).

It is not yet clear that arbitrary partial orders make sense economically, but it is a convenient generalisation for implementation purposes. The smart constructors below implement partial orders that lead to sensible results.

Note that the representation of the partial order by its covers does not enforce that it is antisymmetric. Violating this property may create a cyclic graph, leading to nontermination or other nonsense.

Data stored about each good in a Supply.

Ordering on goods in a Supply.

Make a horizontal supply, where all goods are priced relative to selling nothing at all, using the identity relation as the partial order. The order of the list is unimportant.

Make a vertical supply, where each good is priced relative to the previous element of the list and below all the succeeding elements.

Make horizontal supply curves corresponding to a list of fixed total quantities of each good.

Make a tabular supply, where each element of the outer list of lists gives a vertical column, and the columns themselves are ordered horizontally.

Make a tabular supply, where each element of the outer list of lists gives a vertical column, and the columns themselves are ordered horizontally. A single good is below all the columns.

Look up the supply curve for a particular good, returning the empty supply curve if the good is not available at all.

List all the goods with their corresponding supply curves.

Number of supply curves in the supply.

List all the goods from the supply.

List all goods that are immediate successors of the given good.

List all goods that are (transitively) non-strictly larger than the given good.

Find the good that is the immediate predecessor of the given good, if there is one.

Calculate the set of all "bottom" goods in the supply, i.e. those priced relative to selling nothing at all. This will be all the goods for a horizontal supply, or just the first good for a vertical supply.

Is this good a "bottom" good?

Is this good a "top" good?

Is this supply ordered horizontally?

Is this supply ordered vertically?

Calculate the total quantity available from (the finite parts of) the supply curves for the first goods.

Render a set of supply curves in a vaguely human-readable format.

Given a supply and the amounts allocated to each good, calculate the total allocated to a good and all its successors.

Look up the price of a good relative to the preceding good (or to no sale, if there is no preceding good).

Set the supply of a single good within the set of supply curves.

Find the first good with a decreasing supply curve. For a valid supply this should return Nothing.

Function to rescale a set of supply curves, given a new total size of the supply.

Parameter to control how supply is scaled when a TQSS is in use. See scaleSupply for how this is used.

Multiply all the step lengths in the supply curve by the given scaling factor.

Scale a supply to the given total size. First goods will be scaled in proportion to the new total size. Subsequent goods will be scaled depending on the parameter lambda, which must be in the interval [0,1]:

• lambda = 0 scales all goods in proportion to the new total size;
• lambda = 1 does not scale goods other than the first goods.

Scale the supply curves based on the SupplyScaleLambda, then round the step widths to the ScaleFactor.

Round all the supply curves using ceilingSupplyCurve.

Round the widths of the supply curve steps to a precision given by the ScaleFactor. This rounds upwards the cumulative total width of all the steps.

Generate an arbitrary set of supply curves for the given goods, with either a horizontal or a vertical ordering.

Generate an arbitrary set of supply curves for the given goods, with a supplied generator for supply orderings, as well as generators for the number of steps, step width and step height.

Generate an arbitrary supply curve step, given generators for the step width (quantity available) and height (price margin).

Generate an arbitrary supply curve, given generators for the number of supply curve steps, step width and step height.

Generate an arbitrary finite supply curve, given generators for the number of supply curve steps, step width and step height.